***ANSWERING SESSION*** on Thursday 31 May, 2-4pm and 5-6pm, in B2.06.

Here is the official site from the department.

Time & Place: Tue 12-1 in MS.04, Fri 2-4 in MS.05.

Support classes: Tue 10-11 in MA_B3.01, by Michael Doré.

Assessment: 3-hour examination.

Description:

Linear Analysis extends
Linear Algebra to infinite dimensional vector spaces. Functions form
linear spaces of infinite dimension, and differentiation is a linear
operation. Among the numerous applications of linear analysis is the
study of ODE's and PDE's.

We will introduce Banach and Hilbert spaces, and linear maps (operators) between them. Four major theorems will be discussed: Hahn-Banach, uniform boundedness (Banach-Steinhaus), open mapping, and closed graph. These theorems have interesting consequences, in particular regarding the spectrum of linear operators.

We will introduce Banach and Hilbert spaces, and linear maps (operators) between them. Four major theorems will be discussed: Hahn-Banach, uniform boundedness (Banach-Steinhaus), open mapping, and closed graph. These theorems have interesting consequences, in particular regarding the spectrum of linear operators.

Syllabus:

- Banach spaces
- Baire Category Theorem and its consequences

- Hilbert spaces
- Bounded operators in Hilbert spaces
- Unbounded operators

Assignments:

assignment 1 |
(12.01.07) |

assignment 2 | (19.01.07) |

assignment
3 |
(26.01.07) |

assignment
4 |
(02.02.07) |

assignment
5 |
(09.02.07) |

assignment
6 |
(16.02.07) |

assignment
7 |
(23.02.07) |

assignment
8 |
(02.03.07) |

assignment
9 |
(09.03.07) |

**References**:

- Linear Functional Analysis, by B. P. Rynne and M. A. Youngston, Springer (2001)
- Linear Analysis, by B. Bollobas, Cambridge Univ. Press (1990)
- Introductory Functional Analysis with Applications, by E. Kreyszig, Wiley (1978)
- Functional Analysis,
by K. Yosida, Springer (1980)

- Applied Analysis, by J. K. Hunter and B. Nachtergaele (2001)
- Real Analysis,
by G. B. Folland, Wiley (1999)